Decision making in uncertain and changing environments

We consider an agent who has to repeatedly make choices in an uncertainand changing environment, who has full information of the past, who discountsfuture payoffs, but who has no prior. We provide a learning algorithm thatperforms almost as well as the best of a given finite number of experts orbenchmark strategies and does so at any point in time, provided the agentis sufficiently patient. The key is to find the appropriate degree of forgettingdistant past. Standard learning algorithms that treat recent and distant pastequally do not have the sequential epsilon optimality property.